In a large bowl, place mizithra and feta cheese or a combination of ricotta and feta cheese. Add one egg and mix together using a fork or spoon.
Add finely chopped mint to the mixture and mix thoroughly making sure the mint is well integrated with the cheese and eggs. Set aside.
On a clean floured surface, roll out your phyllo dough using a rolling pin.
Using the 4-inch cookie cutter, cut dough circles and leave them on a lightly floured surface.
As you cut each dough circle, you will have some left over. Add it to the dough and roll it out again until you make about 18 to 22 dough circles.
Take about 1 tablespoon of the cheese mixture and place it in the middle of each dough circle.
Fold the dough over into a half-moon or crescent shape and seal the edges using a cookie cutter or fork.
Heat extra virgin olive oil in a deep saucepan on high heat.
Deep fry the kalitsounia cheese pies in batches, ensuring to turn them over periodically.
Once both sides are golden brown, about 3 to 4 minutes, carefully remove them and place on an absorbent paper towel to drain.
To serve, let the Cretan cheese pie cool and then drizzle honey and enjoy.